A=(({{a/t, b/t}, {c, d}}))

Eigenvectors[A]

MatrixForm /@ JordanDecomposition[A]

DSolve[x y''[x]+ p y'[x] + q y[x]==0, y[x], x]

DSolve[x y'[x]+((E^x)+(E^(-x)))y[x]==0, y[x], x]

Sol=NDSolve[
x y'[x]+((E^x)+(E^(-x)))y[x]==0 && y[1]==1,
y[x], {x,ϵ=(10^(-9)),1}
];
Plot[Evaluate[y[x] /. Sol], {x,ϵ,1}, PlotPoints -> 1000]

Plot[Evaluate[(((y[x]))^(-1/2)) /. Sol], {x,ϵ,1}, PlotPoints -> 1000]